Simulating a local emissions levy to fund local energy effiency retrofit

Focus on: Portsmouth

1 About

This report is based on a model described in a paper presented at the 2021 International Conference on Evolving Cities, University of Southampton, 22 – 24 September 2021.

If you want to cite the method/model please use:

Anderson, B. (2021). Simulating the consequences of an emissions levy at the city and neighbourhood scale. Paper presented at the International Conference on Evolving Cities, MAST Mayflower Studios, Southampton, United Kingdom. 22 - 24 Sep 2021.

2 Citing this report

If you wish to re-use material from this report please cite it as:

Ben Anderson (2021) Simulating a local emissions levy to fund local energy effiency retrofit : Portsmouth. University of Southampton, United Kingdom

License: CC-BY

Share, adapt, give attribution.

3 Highlights

This report estimates the value of an emissions levy using LSOA level data on emissions derived from the CREDS place-based emissions calculator. These emissions are all consumption, gas and electricity. It does this under two scenarios - a simple carbon value multiplier and a rising block tariff.

It then compares these with estimates of the cost of retrofitting EPC band dwellings D-E and F-G in each LSOA and for the whole area under study.

Key results:

• Figure 5.1 shows the LSOA level per dwelling ‘all emissions’ in Tonnes CO2e - which areas emit the most?
• Table 5.6 shows total levy generated under Scenario 1
• Table 5.12 shows total levy generated under Scenario 2
• Table 5.13 shows total retrofit costs and Figure 5.18 shows the LSOA level retrofit costs per dwelling by IMD decile for comparison with Figure 5.1
• Figure 5.19 shows the years to pay back under Scenario 1 for an all emissions levy while * Figure 5.23 does the same for Scenario 2
• Figure 5.21 shows what would happen after year 1 if the levy were shared equally across LSOAs (all emissions, Secenario 1) and Figure 5.25 shows the same for Scenario 2.
• Figure 5.27 shows payback years under each Scenario assuming a constant all emissions levy

4 Introduction

Background blurb about emissions, retofit, carbon tax/levy etc

5 Emissions Levy Case Study: Portsmouth

In the reminder of this paper we develop a model of an emissions levy using LSOA level data on emissions derived from the CREDS place-based emissions calculator.

We apply carbon ‘values’ to a number of emissions categories to estimate the levy revenue that would be generated for each LSOA in year 1 of such a levy. We then sum these values to given an overall levy revenue estimate for the area in the case study.

We then use estimates of the cost of retrofitting EPC band dwellings D-E and F-G together with estimates of the number of such dwellings in each of the LSOAs to calculate the likely cost of such upgrades in each LSOA and for the whole area in the case study.

We then compare the distributions of the two to understand whether sufficient revenue would be generated within each LSOA to enable the per-LSOA or whole case study area costs of the energy efficiency upgrades to be met. In doing so we also analyse the extent to which redistribution of revenue from high emissions areas (households) would be required.

It should be noted that this is area level analysis using mean emissions per household. It will not capture within-LSOA heterogeneity in emissions and so will almost certainly underestimate the range of the household level emissions levy value.

NB: no maps in the interests of speed

5.1 Data

We will use a number of Lower Layer Super Output Area (LSOA) level datasets to analyse the patterns of emissions. Some of these are in the repo as they are public access, others are not (or too large).

• CREDS place-based emissions estimates (contains data from a wide range of sources including https://epc.opendatacommunities.org/ for EPCs)
• 2018 residential gas & electricity use data
• Indices of Deprivation 2019
• Urban/Rural classification at LSOA level
• various LSOA look-up tables from geoportal

All analysis is at LSOA level. Cautions on inference from area level data apply.

5.2 CREDS place-based emissions estimates

See https://www.creds.ac.uk/why-we-built-a-place-based-carbon-calculator/

“The highest carbon areas have an average per person footprint more than eight times larger than the lowest carbon areas.”

“We are not effectively targeting decarbonisation policies in high carbon areas. For example, the recently collapsed Green Homes Grants scheme provided a grant to cover 66% of the cost (up to £5,000) of retrofitting homes. For people claiming certain benefits, the cap was raised to 100% and £10,000. But the calculator shows that the big polluters are the large homes in very wealthy areas. In these neighbourhoods, the issue is not affordability but motivation. For high income households, energy costs are a small proportion of their expenditure and so the cost savings for retrofitting their home are inconsequential. As there are no policy “sticks” to incentivise action in the collective interest it is unsurprising that high carbon neighbourhoods have not prioritised decarbonisation."

Source: https://www.carbon.place/

Notes:

• Emissions are presented as per capita…
• Appears to be based on residential/citizen emissions only - does not appear to include commercial/manufacturing/land use etc

Now we need to convert the per capita to totals and then use the number of electricity meters as a proxy for the number of dwellings

Ideally we’d have Census 2021 data but we don’t have it yet. So instead we’ll use the number of electricity meters for 2018 which aligns with the CREDS data (might be an over-estimate if a dwelling has 2…)

First check the n electricity meters logic…

##           LSOA11NM                  WD18NM nGasMeters nElecMeters epc_total
## 1: Portsmouth 017D                  Milton        937        1153       895
## 2: Portsmouth 024B                 St Jude        936        1255       973
## 3: Portsmouth 014F                 Baffins        931         942       536
## 4: Portsmouth 023B Eastney and Craneswater        909         953       571
## 5: Portsmouth 022C                 St Jude        853        1000       870
## 6: Portsmouth 002A                  Cosham        850         914       635

##           LSOA11NM                  WD18NM nGasMeters nElecMeters epc_total
## 1: Portsmouth 024B                 St Jude        936        1255       973
## 2: Portsmouth 024A Eastney and Craneswater        702        1176       963
## 3: Portsmouth 017D                  Milton        937        1153       895
## 4: Portsmouth 024E               St Thomas        306        1012       784
## 5: Portsmouth 022C                 St Jude        853        1000       870
## 6: Portsmouth 004C              Paulsgrove        463         999       575

Check that the number of electricity meters reasonably correlates with the number of EPCs from the CREDS data. We would not expect the number of gas meters to correlate due to non-gas dwellings etc.

There may also be difficulties where there are multiple meters per property - e.g. one ‘standard’ and one ‘economy 7.’ Really should switch to using address counts from postcode file.

Check that the assumption seems sensible…

Check for outliers - what might this indicate?

5.2.1 Estimate per dwelling emissions

We want to present the analysis in ‘per dwelling’ or ‘per household’ terms so we need to convert the total kg CO2e values to per dwelling values by dividing by the number of electricity meters.

## # Summary of per dwelling values

Table 5.2: Data summary

Name	…[]
Number of rows	125
Number of columns	9
Key	NULL
_______________________
Column type frequency:
numeric	9
________________________
Group variables	None

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
CREDStotal_kgco2e_pdw	0	1	17285.30	6564.15	6065.37	12696.72	17132.42	20232.04	45546.56	▅▇▂▁▁
CREDSgas_kgco2e2018_pdw	0	1	1953.64	500.56	353.62	1736.43	1997.90	2265.41	3315.13	▁▂▇▅▁
CREDSelec_kgco2e2018_pdw	0	1	934.83	139.62	705.45	866.73	916.18	992.76	1816.82	▇▅▁▁▁
CREDSmeasuredHomeEnergy_kgco2e2018_pdw	0	1	2888.48	536.17	1524.54	2620.31	2903.72	3185.37	4563.92	▂▅▇▂▁
CREDSotherEnergy_kgco2e2011_pdw	0	1	65.05	85.49	5.63	28.07	46.16	72.48	696.52	▇▁▁▁▁
CREDSallHomeEnergy_kgco2e2018_pdw	0	1	2953.53	497.23	1574.89	2686.30	2958.28	3223.52	4593.58	▁▅▇▂▁
CREDScar_kgco2e2018_pdw	0	1	1710.34	550.06	457.84	1376.08	1751.80	2027.31	3521.34	▂▆▇▂▁
CREDSvan_kgco2e2018_pdw	0	1	540.81	2878.29	43.32	144.88	203.43	295.79	32186.23	▇▁▁▁▁
CREDSpersonalTransport_kgco2e2018_pdw	0	1	2251.15	2883.36	528.81	1602.54	1967.47	2312.95	33215.59	▇▁▁▁▁

Examine patterns of per dwelling emissions for sense.

5.2.1.1 All emissions

Figure 5.1 shows the LSOA level per dwelling ‘all emissions’ in Tonnes CO2e as estimated by the CREDS tool against the Index of Multiple Deprivation (IMD) score and uses the size of the points to represent the % of dwellings with electric heating. Colour is used to represent the IMD decile where decile 1 is the 10% least deprived.

## Per dwelling T CO2e - all emissions

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.1: Scatter of LSOA level all per dwelling emissions against IMD score

## Correlation test (pwcorr)

## 
##  Pearson's product-moment correlation
## 
## data:  selectedLsoasDT$IMDScore and selectedLsoasDT$CREDStotal_kgco2e_pdw
## t = -8.2065, df = 123, p-value = 2.586e-13
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6975637 -0.4681088
## sample estimates:
##        cor 
## -0.5948201

## Total emissions per dwelling (LSOA level) summary

##    LSOA11CD            WD18NM                       IMD_Decile_label All_Tco2e_per_dw
##  Length:125         Length:125         4                    :29      Min.   : 6.065  
##  Class :character   Class :character   5                    :21      1st Qu.:12.697  
##  Mode  :character   Mode  :character   1 (10% most deprived):15      Median :17.132  
##                                        2                    :15      Mean   :17.285  
##                                        3                    :14      3rd Qu.:20.232  
##                                        6                    :12      Max.   :45.547  
##                                        (Other)              :19

5.2.1.2 Home energy use

Figure 5.2 uses the same plotting method to show emissions per dwelling due to gas use.

## Per dwelling T CO2e - gas emissions

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   353.6  1736.4  1997.9  1953.6  2265.4  3315.1

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.2: Scatter of LSOA level gas per dwelling emissions against IMD score

## Correlation test (pwcorr)

## 
##  Pearson's product-moment correlation
## 
## data:  selectedLsoasDT$IMDScore and selectedLsoasDT$CREDSgas_kgco2e2018_pdw
## t = -7.2718, df = 123, p-value = 3.613e-11
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6603430 -0.4124235
## sample estimates:
##        cor 
## -0.5483192

Figure 5.3 uses the same plotting method to show emissions per dwelling due to electricity use.

## Per dwelling T CO2e - elec emissions

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.3: Scatter of LSOA level elec per dwelling emissions against IMD score - who emits?

## Correlation test (pwcorr)

## 
##  Pearson's product-moment correlation
## 
## data:  selectedLsoasDT$IMDScore and selectedLsoasDT$CREDSelec_kgco2e2018_pdw
## t = -4.6008, df = 123, p-value = 1.031e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.5235574 -0.2225472
## sample estimates:
##        cor 
## -0.3831797

Figure 5.4 uses the same plotting method to show emissions per dwelling due to other energy use. This should be higher for off-gas areas which tend to be rural areas so we also present analysis by the LSOA’s urban/rural classification.

## Per dwelling T CO2e - elec emissions

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.4: Scatter of LSOA level other energy per dwelling emissions against IMD score - who emits?

## Correlation test (pwcorr)

## 
##  Pearson's product-moment correlation
## 
## data:  selectedLsoasDT$IMDScore and selectedLsoasDT$CREDSelec_kgco2e2018_pdw
## t = -4.6008, df = 123, p-value = 1.031e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.5235574 -0.2225472
## sample estimates:
##        cor 
## -0.3831797

Check whether all measured energy emissions combined (gas & electricity) correlate with all emissions (in this data).

## 
##  Pearson's product-moment correlation
## 
## data:  selectedLsoasDT$CREDStotal_kgco2e_pdw and selectedLsoasDT$CREDSmeasuredHomeEnergy_kgco2e2018_pdw
## t = 12.762, df = 123, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.6676956 0.8215174
## sample estimates:
##       cor 
## 0.7548009

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Do we see strong correlations? If so in theory we could (currently) use measured energy emissions as a proxy for total emissions.

Repeat for all home energy - includes estimates of emissions from oil etc

## 
##  Pearson's product-moment correlation
## 
## data:  selectedLsoasDT$CREDStotal_kgco2e_pdw and selectedLsoasDT$CREDSallHomeEnergy_kgco2e2018_pdw
## t = 12.719, df = 123, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.6662992 0.8206979
## sample estimates:
##       cor 
## 0.7537165

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

How does the correlation look now?

5.2.1.3 Transport

We don’t expect to use this data as it is already taxed in a way that relates to emissions (?)

Figure 5.5 uses the same plotting method to show emissions per dwelling due to van use. Again, we present analysis by the LSOA’s urban/rural classification.

## Per dwelling T CO2e - car emissions

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.5: Scatter of LSOA level car use per dwelling emissions against IMD score

## Correlation with IMD score (pwcorr)

## 
##  Pearson's product-moment correlation
## 
## data:  selectedLsoasDT$IMDScore and selectedLsoasDT$CREDScar_kgco2e2018_pdw
## t = -10.658, df = 123, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.7742914 -0.5889535
## sample estimates:
##        cor 
## -0.6928982

Figure 5.6 uses the same plotting method to show emissions per dwelling due to van use.

## Per dwelling T CO2e - van emissions

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.6: Scatter of LSOA level van use per dwelling emissions against IMD score

## Correlation with IMD score (pwcorr)

## 
##  Pearson's product-moment correlation
## 
## data:  selectedLsoasDT$IMDScore and selectedLsoasDT$CREDSvan_kgco2e2018_pdw
## t = 0.91534, df = 123, p-value = 0.3618
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.09472168  0.25418994
## sample estimates:
##        cor 
## 0.08225404

5.2.2 Impute EPC counts

In order to estimate the LSOA level retrofit costs, we need to impute the EPC counts in each LSOA. We do this using the number of electricity meters as the presumed number of dwellings and the observed % of EPCs in each band for all dwellings with EPCs which is provided by the CREDS data. This assumes that if we had EPCs for all dwellings then the % in each band in each LSOA would stay the same. This is quite a bold assumption…

Note that the EPC database is continuously updated so more recent upgrades will not be captured in the data used for this analysis. This means the total retrofit costs are likely to be an over-estimate. The extent of this over-estimate would require the use of an updated (current) EPC data extract and is left for future work.

## N EPCs

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   222.0   346.0   447.0   458.5   536.0   973.0

## N elec meters

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   494.0   644.0   695.0   726.8   800.0  1255.0

Correlation between high % EPC F/G or A/B and deprivation?

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Now we need to convert the % to dwellings using the number of electricity meters (see above).

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

5.2.3 Estimating the annual emissions levy

Case studies:

• Annual carbon tax
• Half-hourly (real time) carbon tax (not implemented) - this would only affect electricity

BEIS/ETC Carbon ‘price’

• 2020 - £21.93 https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/849276/Carbon__Penalty_Price_Determination_for_2020.pdf

EU carbon ‘price’

• September 2021: €60 (£51) https://tradingeconomics.com/eecxm:ind

BEIS Carbon ‘Value’ https://www.gov.uk/government/publications/valuing-greenhouse-gas-emissions-in-policy-appraisal/valuation-of-greenhouse-gas-emissions-for-policy-appraisal-and-evaluation#annex-1-carbon-values-in-2020-prices-per-tonne-of-co2

• based on a Marginal Abatement Cost (MAC)
• 2021:
  • Low: £122/T
  • Central: £245/T <- use the central value for now
  • High: £367/T

Scenario 1: apply the central value Scenario 2: apply the low/central/high as a rising block tariff for each emissions source. Set threhsolds to 33% and 66% (in absence of any other guidance!)

5.2.3.1 Scenario 1: Central cost

Table 5.6 below shows the overall £ GBP total for the case study area in £M under Scenario 1.

Figure 5.7: Proportion of total emissions due to gas & electricity use by region covered

The table below shows the mean per dwelling value rounded to the nearest £10.

Figure ?? shows the total £k per LSOA and £ per dwelling revenue using BEIS central carbon price plotted against IMD score. The tables show the LSOAs with the highest and lowest values.

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.8: £k per LSOA revenue using BEIS central carbon price

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.9: £k per LSOA revenue using BEIS central carbon price

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1486    3111    4197    4235    4957   11159

Figure ?? repeats the analysis but just for gas.

Anything unusual?

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.10: £k per LSOA incurred via gas using BEIS central carbon price

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.11: £k per LSOA incurred via gas using BEIS central carbon price

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   86.64  425.43  489.48  478.64  555.02  812.21

Figure ?? repeats the analysis for electricity.

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.12: £k per LSOA incurred via electricity using BEIS central carbon price

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.13: £k per LSOA incurred via electricity using BEIS central carbon price

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   172.8   212.3   224.5   229.0   243.2   445.1

Figure ?? shows the same analysis for measured energy (elec + gas)

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.14: £k per LSOA incurred via electricity and gas using BEIS central carbon price

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.15: £k per LSOA incurred via electricity and gas using BEIS central carbon price

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   373.5   642.0   711.4   707.7   780.4  1118.2

5.2.3.2 Scenario 2: Rising block tariff

Applied to per dwelling values (not LSOA total) - may be methodologically dubious?

Cut at 25%, 50% - so any emissions over 50% get high carbon cost

## Cuts for total per dw

##        0%       25%       50%       75%      100% 
##  6065.372 12696.716 17132.420 20232.036 45546.559

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Table 5.10: Data summary

Name	…[]
Number of rows	125
Number of columns	3
Key	NULL
_______________________
Column type frequency:
numeric	3
________________________
Group variables	None

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
V1	0	1	17.29	6.56	6.07	12.7	17.13	20.23	45.55	▅▇▂▁▁
beis_GBPtotal_sc2_perdw	0	1	3067.13	2007.88	739.98	1549.0	2626.18	3773.31	13063.74	▇▃▁▁▁
beis_GBPtotal_sc2	0	1	2094440.42	1144173.96	587844.80	1257978.6	1944245.61	2520568.28	6453485.42	▇▇▂▁▁

Figure 5.16 compares the £ levy under each scenario for all consumption.

Figure 5.16: Comparing £ levy under each scenario

## [1] 25.93655

## [1] 13.15284

##        region nLSOAs sumAllConsEmissions_GBP sumGasEmissions_GBP sumElecEmissions_GBP sumPop
## 1: South East    125                261.8051            25.93655             13.15284 215160

Figure 5.17: Contribution to sum levy £ GBP by source

5.2.4 Estimate retofit costs

• from A-E <- £13,300
• from F-G <- £26,800

Source: English Housing Survey 2018 Energy Report

Model excludes EPC A, B & C (assumes no need to upgrade)

Adding these back in would increase the cost… obvs

Table 5.13 reports total retofit costs.

## To retrofit D-E (£m)

## [1] 720.2602

## Number of dwellings: 54155

## To retrofit F-G (£m)

## [1] 81.756

## Number of dwellings: 3051

## To retrofit D-G (£m)

## [1] 802.0162

## To retrofit D-G (mean per dwelling)

## [1] 13983

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.18 shows the LSOA level retofit costs per dwelling by IMD decile.

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.18: LSOA level retofit costs per dwelling by IMD score

5.2.5 Compare levy with costs

5.2.5.1 Scenario 1

Totals

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Repeat per dwelling

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

5.2.5.2 Scenario 2

Totals

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Repeat per dwelling

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

5.2.6 Years to pay…

5.2.6.1 Scenario 1

Figure 5.19 shows years to pay under Scenario 1 (all emissions)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.245   2.824   3.326   3.828   4.512   9.306

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.19: Years to pay under Scenario 1 (all em issions)

## Median years: 3.33

Figure 5.20 shows years to pay under Scenario 1 (energy emissions)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   13.05   17.81   19.56   20.53   21.58   37.03

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.20: Years to pay under Scenario 1 (energy emissions)

## Median years: 19.56

Figure 5.21 shows the year 1 outcome if levy is shared equally (all emissions levy).

Figure 5.21: Year 1 outcome if levy is shared equally (all emissions levy)

Figure 5.22 shows the year 1 outcome if levy is shared equally (energy emissions levy).

Figure 5.22: Year 1 outcome if levy is shared equally (energy emissions levy)

What happens in Year 2 totally depends on the rate of upgrades… given the supply chain & capacity issues it’s likely that the levy would build up a substantial ‘headroom’ that could then be spent over time…

5.2.6.2 Scenario 2

Figure 5.23 shows years to pay under Scenario 2 (all emissions)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.064   3.703   5.269   6.564   9.058  18.689

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.23: Years to pay under Scenario 2 (all em issions)

## Median years: 5.27

Figure 5.24 shows years to pay under Scenario 2 (energy emissions)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   13.05   17.81   19.56   20.53   21.58   37.03

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 5.24: Years to pay under Scenario 2 (energy emissions)

Figure 5.25 shows the year 1 outcome if levy is shared equally (all emissions levy).

Figure 5.25: Year 1 outcome if levy is shared equally (all emissions levy)

Figure 5.26 shows the year 1 outcome if levy is shared equally (energy emissions levy).

Figure 5.26: Year 1 outcome if levy is shared equally (energy emissions levy)

What happens in Year 2 totally depends on the rate of upgrades…

5.2.6.3 Compare scenarios

Figure 5.27 compares pay-back times for the two scenarios - who does the rising block tariff help?

Figure 5.27: Comparing pay-back times across scenarios

x = y line shown for clarity

6 R environment

6.1 R packages used

• base R (R Core Team 2016)
• bookdown (Xie 2016a)
• data.table (Dowle et al. 2015)
• ggplot2 (Wickham 2009)
• kableExtra (Zhu 2018)
• knitr (Xie 2016b)
• rmarkdown (Allaire et al. 2018)
• skimr (Arino de la Rubia et al. 2017)

6.2 Session info

7 Data Tables

I don’t know if this will work…

## Doesn't

References

Allaire, JJ, Yihui Xie, Jonathan McPherson, Javier Luraschi, Kevin Ushey, Aron Atkins, Hadley Wickham, Joe Cheng, and Winston Chang. 2018. Rmarkdown: Dynamic Documents for r. https://CRAN.R-project.org/package=rmarkdown.

Arino de la Rubia, Eduardo, Hao Zhu, Shannon Ellis, Elin Waring, and Michael Quinn. 2017. Skimr: Skimr. https://github.com/ropenscilabs/skimr.

Dowle, M, A Srinivasan, T Short, S Lianoglou with contributions from R Saporta, and E Antonyan. 2015. Data.table: Extension of Data.frame. https://CRAN.R-project.org/package=data.table.

R Core Team. 2016. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.

Wickham, Hadley. 2009. Ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. http://ggplot2.org.

Xie, Yihui. 2016a. Bookdown: Authoring Books and Technical Documents with R Markdown. Boca Raton, Florida: Chapman; Hall/CRC. https://github.com/rstudio/bookdown.

———. 2016b. Knitr: A General-Purpose Package for Dynamic Report Generation in r. https://CRAN.R-project.org/package=knitr.

Zhu, Hao. 2018. kableExtra: Construct Complex Table with ’Kable’ and Pipe Syntax. https://CRAN.R-project.org/package=kableExtra.